Question

Find the value of $(66{)}^2$ by visualizing the identity $(a+b{)}^2=a^2+2ab+b^2$.

• A. $5,336$
• B. $3,456$
• C. $5,676$
• D. $4,356$

Answer 1

The correct option is D $4,356$

We have to find value of $(66{)}^2$. So, let us visualize this with the help of diagram.


$66$ can also be written as $(60+6)$.

So, the value of $(66{)}^2$ will be area of square PQRS.

$\Rightarrow$Area of square PQRS $=(60+6)(60+6)=(60+6{)}^2$sq.units.

It can also be written as
Area of square PQRS = Area of Red square + Area of Orange and White rectangles + Area of Blue square

Orange and white rectangles have similar dimensions.
So, area of orange and white rectangles $=(60\times 6)$ sq.units.

Area of blue square is $=(6\times 6)$ sq.units.

And, Area of red square $=(60\times 60)$ sq.units

Now, $\Rightarrow (60+6{)}^2=60\times 60+60\times 6+60\times 6+6\times 6)$

$\Rightarrow (60+6{)}^2=(60{)}^2+2\times 60\times 6+6^2$

$\Rightarrow (60+6{)}^2=3,600+720+36=4,356.$sq.units.

$\Rightarrow (66{)}^2=4,356$

$\therefore$ Required value of $(66{)}^2$ is $4,356$.